Solve the V* values for this MDP

Question

For the given MDP, find the values for the states S2, S3 and S4. States S1 and S5 are terminal states with values 0 and 1 respectively. Living Reward (R) is 0. Transition function is defined as follows: When going Left or Right, there is a 90% probability that the move goes as planned and 10% probability that no move occurs. Discount rate gamma is 0.9

S1	S2	S3	S4	S5
0	x2	x3	x4	1

Answer 1

x4 = 0 + 0.9(0.9 * 1 + 0.1 *  x4) => 0.91*x4 = 0.81 => x4 = 81/91 = 0.890109

x3 = 0 + 0.9(0.9 * x4 + 0.1* x3) => 0.91 * x3 = 0.81 * x4 => x3 = (81/91)^2 = 0.792295

x2 = 0 + 0.9(0.9 * x3 + 0.1 * x2) => 0.91 *x2 = 0.81 * x3 => x2 = (81/91)^3 = 0.7052301